Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
200 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 43 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #21419421 | C3 | semidirect |
| 2. #21419404 | C3 | semidirect |
| 3. #21419362 | C3 | semidirect |
| 4. #21419283 | C3 | semidirect |
| 5. #21419273 | C3 | semidirect |
| 6. #21419271 | C3 | semidirect |
| 7. #21419264 | C3 | semidirect |
| 8. #21419263 | C3 | semidirect |
| 9. C31×#6883 | C3 | semidirect |
| 14. #14578902 | C32 | semidirect |
| 16. #14578900 | C32 | semidirect |
| 20. #14578886 | C32 | semidirect |
| 22. C9×C31⋊C9 | C32 | semidirect |
| 23. C31×#733 | C32 | semidirect |
| 25. C31×C9⋊C9 | C32 | semidirect |
| 63. #6883 | C31⋊C3 | semidirect |
| 79. #733 | C3×C31⋊C3 | semidirect |
| 88. C9⋊C9 | C3×C31⋊C3 | semidirect |
| 90. C31 | #10624851 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21419421 | 3 |
| #21419404 | 3 |
| #21419362 | 3 |
| #21419283 | 3 |
| #21419273 | 3 |
| #21419271 | 3 |
| #21419264 | 3 |
| #21419263 | 3 |
| C31×#6883 | 3 |
| #10624851 | 31 |